2014-2015 Academic Year Fall Term
EE445 HOMEWORK I (Ten Problems).
1-For the given primitive flow table below;
a) Find any equivalent states. b) Draw the merger diagram and merge compatible states to
form minimum number of states. c) Assign outputs to unstable states of the reduced flow table
avoiding false outputs. Transitions should occur as quick as possible.
00
01
11
10
z
a
a
b
-
c
0
b
a
b
d
-
0
c
f
-
e
c
1
d
-
b
d
g
0
e
-
h
e
c
1
f
f
b
-
c
1
g
a
-
d
g
0
h
f
h
e
-
1
2- Make the following state table race free. The solution should have minimum number of
states.
0
1
00
10
00
01
01
00
11
01
11
10
01
11
3- Assign state codes to each state using two state variables avoid only critical races.
00
01
11
10
A
A
B
B
A
B
B
D
B
C
C
C
C
B
A
D
C
D
B
A
4- Find a circuit that has no static hazard and implements the Boolean function below.
Assume fundamental mode of operation.
F(A,B,C,D)=  (0,1,5,7,8,9)
5- a) Find a race free state assignment for the reduced flow table below, show resulting
state transition table.
b) Assume the state assignment for the given flow table is as; a=00, b=01, c=11, and d=10.
Make the necessary changes in the flow table in order to get rid of races without changing
the operation of the circuit.
00
01
11
10
a
a
c
a
d
b
b
d
a
b
c
b
d
c
b
d
a
d
c
d
X,Y
6- Assume there is a voting cabin that only one voter can use at a time. The cabin has two
doors; an entrance E and the exit X. An open door corresponds to logic level 1, and a closed
door to 0. A light L on the entrance indicates whether the cabin is occupied. The lamp is
initially green(logic level 0); it turns to red(logic level 1) after the entrance door is opened and
than closed; and it turns green again after the exit door is opened and than closed. There is
also an alarm A which is activated(logic level 1) if the above order is violated; that is if the
entrance door is opened while the cabin is occupied or the exit door is opened while it is
vacant. Once the alarm starts it does not stop until the officials reset the system; so the
“alarm “ state is a dead end. Obtain a primitive flow table for the circuit in minimal form.
Assume two doors can not be opened simultaneously.
7- For the system in question 6; a) Find a flow table in minimal row. B) Make state
assignments and obtain expressions for the S and R inputs for the implementation of the
circuit with NOR SR latches. C( obtain the expressions for L and A. Do not allow hazards to
occur in the case of L due to single input changes.
8-An asynchronous sequential circuit has two inputs A and B, and an output Z. Merge the
primitive flow table to minimal non-mixed output form.
00
01
11
10
a
a,0
b,-
-,-
c,-
b
-,-
b,1
d,-
-,-
c
-,-
-,-
d,-
c,1
d
-,-
f,-
d,0
e,-
e
a,0
-,-
-,-
e,0
f
a,-
f,0
-,-
-,-
A,B
9- Implement the circuit in question 8 by using NOR SR latches. Try to make the circuit
minimal and the output false free.
10- An asynchronous circuit with inputs A,B and output z working in its fundamental mode
will be designed. “The output becomes 1 after two consecutive changes occur in A while B
remains at logic 1. Then to obtain next z=1; B must change from 1 to 0 than to 1 and another
consecutive changes in A should occur while B remains at logic 1. For all other cases output
will remain at 0. Find a minimal primitive flow table and merge it to minimal row non-mixed
output flow table.